Based on structural information from X-ray and NMR experiments, computational simulations performed us- ing molecular dynamics and the quantum mechanical/molecular mechanical (QM/MM) approach are able to describe the chemical reactions and redox processes catalyzed by enzymes. Ab initio QM/MM methods capitalize on the accuracy and reliability of the associated quantum mechanical approaches, however at a much higher computational cost compared with corresponding semiempirical quantum mechanical ap- proaches. Thus reaction path and free energy calculations based on ab initio QM/MM methods encounter unique challenges in simulation times and phase space sampling. This proposal aims to develop further the ab initio QM/MM methodology and its application to the studies of redox processes and mechanisms of chemical reactions in important enzymes. The long-term goal is to develop and establish density functional theory-based QM/MM simulation as an equal partner with experiments for the study of enzymes and to provide detailed insight into chemical reaction and redox reaction mechanisms in biological systems. The ab initio QM/MM-MFEP method has been developed recently to overcome some of the difficul- ties encountered in previous ab initio QM/MM approaches for obtaining minimum energy reaction paths. This proposal aims to develop the QM/MM-MFEP method further into a comprehensive and accurate method for the simulation of redox processes in solution and in enzymes using ab initio QM/MM meth- ods. The QM/MM methodology will be used to investigate several important systems: (1) The redox poten- tials in wild-type and single-site variants of the copper protein enzyme peptidyglycine alpha-hydroxylating monooxygenase (PHM), which is a prototype for the two copper family enzymes that includes dopamine beta-monooxygenase and tyramine beta-monooxygenase. (2) Human DNA polymerase , which catalyzes the phosphoryl-transfer reaction in DNA synthesis. (3) Sulfatases, which controls the state of sulfation of proteins, carbohydrates, lipids and steroids, and may produce the largest rate enhancements that are generated by any enzyme. (4) Peptidoglycan recycling enzyme, which catalyze phosphoryl transfer and hydrolysis. The proposed work will lead to the advancement of theoretical and computational methodology and the understanding of important enzyme reaction mechanisms. In addition, it will also serve to aid in the design of new drugs and enzyme inhibitors.